Not evaluated
The Gaussian moat conjecture (family 028)
The gist
In its release of October 6, 2026, OpenAI presents, for the Gaussian moat conjecture, a manuscript on bounded-step walks on Gaussian primes.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-028-gaussian-moat-conjecture-r1
@misc{discoveria-oai-fam-028-gaussian-moat-conjecture-r1,
author = {{DiscoverIA}},
title = {The Gaussian moat conjecture (family 028)},
howpublished = {DiscoverIA registry, entry oai-fam-028-gaussian-moat-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-028-gaussian-moat-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript were correct, it would address the question this conjecture asks: can one travel across the plane by hopping from one Gaussian prime to the next, with steps of bounded length? A Gaussian prime is a complex number a + bi, with a and b integers, that does not factor into a product of such numbers.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI itself; no third-party check is recorded. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 028.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Bounded-Step-Walks-on…link only, reading not recorded
- Lean proofgithub.com · 028.mdpage read word for word
- Lean proofgithub.com · GaussianMoat.leanlink only, reading not recorded
Method
According to OpenAI, an unreleased internal model produced it. The openai/math repository holds the manuscript “Bounded-Step Walks on Gaussian Primes” (September 26, 2026) and lean/docs/028.md, with 1 Comparator statement (GaussianMoat.lean). The file formalization.yaml carries “review: status: unchecked” and lists this family among its sources; history.md reports no revision of the manuscript. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Number theory)
- In openai/math
- family 028, section “Number theory”, 1 manuscript dated Sep 26, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 28 of 372, by family number
- Not evaluated : Erdős’s short Egyptian-fraction conjecture (family 025)
- Not evaluated : Positive lower density of large prime gaps (family 026)
- Not evaluated : Integral density on curve character varieties (family 027)
- Not evaluated : The Gaussian moat conjecture (family 028)
- Not evaluated : Artin's primitive root conjecture: infinitude for every base (family 029)
- Not evaluated : Modularity over imaginary quadratic fields (family 030)
- Not evaluated : Uchida's conjecture for open Galois homomorphisms (family 031)
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